<TITLE>prob007: all-interval series</TITLE>
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<H1>prob007: all-interval series</H1>

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<TR> <TD> proposed by
     <TD ALIGN=LEFT> <A HREF="http://www.cs.ubc.ca/spider/hoos/">
          <B>Holger Hoos</B></A> 
          <ADDRESS><a href="mailto:hoos@cs.ubc.ca">
          hoos@cs.ubc.ca</a></ADDRESS>
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<H3> References </H3>

The musical all-interval series have a certain prominence
in serial composition; they can be traced back
to Alban Berg and have been extensively studied and used
by Ernst Krenek, for example, in his orchestral piece op.170,
``Quaestio temporis'' (A Question of Time).

<P>

Hoos describes the generalization of the problem
and its formulation as a CSP and SAT problem in his PhD thesis:


<P>
<A HREF="http://www.cs.ubc.ca/spider/hoos/publ-ai.html#phd">
Stochastic Local Search - Methods, Models, Applications (PhD thesis, TU Darmstadt, 1998)</A>
<P>

Simonis and Beldiceanu have shown that, using global constraints,
CHIP can find one solution without search. Finding all solutions
remains more of a challenge.



<P>
<A HREF="helmut.pdf">
A note on CSPLIB prob007</A>, by Simonis and Beldiceanu.

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